[8.05] A fully analytical approach to the harmonic development of the tide-generating potential accounting for precession, nutation, and perturbations due to figure and planetary terms.

The development of the tide generating potential (TGP) was
first carried out in harmonic form by Doodson in 1921. In
the recent decades Doodson's 388 tidal constituents of
theTGP have been extended to reach the level of several
thousand partial waves. While a few authors follow Doodson's
analytical approach, the longest expansions all utilize a
numerical filtering approach and a numerical lunisolar
ephemeris. The need for such extended schedule of tidal
constituents is required by the accuracy attained in modern
applications, such as the detection of the motion of the
Earth's core, the reduction of gravimetric measurements and
the computations of tidal perturbations on satellites. The
availability of modern algebraic manipulation systems and of
an accurate theory of the lunar motion can make the daunting
task of the elaborate analytical computations leading to the
TGP an almost trivial matter. It is shown in this paper that
the application of the Wigner's rotation theorem for
spherical harmonics can be invoked to transform the Sun's
and the Moon's motions from the ecliptical to the equatorial
system in a manner perfectly adaptable to algebraic
manipulation up to any desired spherical harmonics degree.
It is also shown that the formulation proposed can easily
handle the accurate modelling of the precessional and
nutational motions of the Earth and the perturbations due to
the figure of the Earth as well as the perturbations due to
the planets, both direct and indirect.

The author(s) of this abstract have provided an email address
for comments about the abstract:
casotto@pd.astro.it